activity-6-and-7-1

Question 1 Suppose the breathing rates of human adults per minute is approximately normal with mean of 16 and standard deviation 0f 4. If a person is selected at random from a sample of 500 persons. a. What is the probability that the breathing rates of the person selected exceed 22? _____  b. How many persons have breathing rates between 19 and 25? _____ Response: 0.0668 Response: 108 

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Question 2 The cerebral blood flow (CBF) in the brains of healthy people is normally n ormally distributed with mean of 74 and a standard deviation of 16. In a sample of 1000 people a. What is the proportion of healthy people will have CBF readings below 100? _____  b. How many healthy people from the sample will have CBF readings between 60 and 80? ____ _ Response: 0.9484 Response: 459 

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Question 3 A psychological introvert-extrovert test produced scores that had a normal distribution with a mean and standard deviation of 80 and 15, respectively. If a person is selected at random from 500 persons. a. What is the probability that the person chosen had a score exceeding 120? _____  b. How many persons had a score between 89 and 104? ___ __ Response: 0.0038 Response: 110 

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Question 4 The mean weight of 500 male students at a certain college is 152 lb. And the standard deviation is 15 lb. Assume that the weights are normally distributed. 1. How many students weigh between 120 and 155 lb? _____

2. What is the probability that a randomly selected male student weighs less than 128 pounds?  _____ Response: 282 Response: 0.0548 

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Question 5 The mean weight of 500 female students at a certain college is 152 lb. And the standard deviation is 20 lb. Assume that the weights are normally distributed. 1. How many students weigh between 120 and 155 lb? _____ 2. What is the probability that a randomly selected fe male student weighs less than 128 pounds?  _____ Response: 253 Response: 0.1151 

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ACTIVITY 7

Question 1 Break downs occur on an old car with rate λ= 5 break -downs/month. The owner of the car is planning to have a trip on his car for 4 days.What is the probability that he will return home safely on his car. (Use the conversion of 30 days in a month.)

Response: 0.5134 

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Question 2 Suppose you usually get 3 phone calls per hour. Compute the probability that a phone call will arrive within the next hour. Response: 0.717 

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Question 3 Commonly, car cooling systems are controlled by electrically driven fans. Assuming that the lifetime T in hours of a particular make of fan can be modeled by an exponential distribution with λ = 0.0003. Find the proportion of fans which will give at most 1000 hours service. Response: 0.950 

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Question 4 Suppose that the amount of time one spends in a bank is exponentially distributed with mean 20 minutes. What is the probability that a customer will spend more than 20 minutes in the bank given that he is still in the bank after 15 minutes? Response: 47.2% 

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Question 5 In a local bar and restaurant, students arrive according to an exponential distribution at a mean rate of 20 students per hour. What is the probability that the waiter has to wait not more than 4 minutes to serve the next student? Response: 26.4%

Question 1 Break downs occur on an old car with rate λ= 5 break -downs/month. The owner of the car is planning to have a trip on his car for 4 days.What is the probability that he will return home safely on his car. (Use the conversion of 30 days in a month.)

Response: 0.5134 

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Question 2 Suppose that the amount of time one spends in a bank is exponentially distributed with mean 20 minutes. What is the probability that a customer will spend more than 20 minutes in the bank given that he is still in the bank after 15 minutes? Response: 52.8% 

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Question 3 The time required to repair a machine is an exponential random variable with rate of 0.7 downs/hour. What is the probability that the repair time will take at least 2 hours given that the repair man has been working on the machine for 45 mins? Response: 0.5831 

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Question 4 The weekly rainfall totals for a section of the mid-western United States follows an exponential distribution with a mean 1.6 inches. Find the probability that a weekly rainfall total in this section will exceed 2 inches. Response: 0.7135 

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Question 5 Suppose that the distance that can covered by a particular car before its battery wears out is exponentially distributed with an average of 10,000 kilometers. The owner of the car needs to take a 5000-km trip. What is the probability that he will be able to complete the trip without having to replace the car battery? Response: 39%

Question 1 Commonly, car cooling systems are controlled by electrically driven fans. Assuming that the lifetime T in hours of a particular make of fan can be modeled by an exponential distribution with λ = 0.0003. Find the proportion of fans which will give at most 1000 hours service. Response: 0.050 

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Question 2 A sugar refinery has three processing plants, all receiving raw sugar in bulk. The amount of raw sugar (in tons) that one plant can process in one day can be modeled using an exponential distribution with mean of 4 tons for each of three plants. If each plants operates independently, find the probability that any given plant processes less than 5 tons of raw sugar on a given day.

Response: 0.2865 

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Question 3 The time required to repair a machine is an exponential random variable with rate of 0.7 downs/hour. What is the probability that a repair time exceeds 2 hours? Response: 0.9426 

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Question 4 The time required to repair a machine is an exponential random variable with rate of 0.7 downs/hour. What is the probability that the repair time will take at most 2 hours given that the repair man has been working on the machine for 30 mins? Response: 0.35 

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Question 5 The weekly rainfall totals for a section of the mid-western United States follows an exponential distribution with a mean 1.6 inches. Find the probability that a weekly rainfall total in this section will exceed 2 inches. Response: 0.2865

Question 1 The time required to repair a machine is an exponential random variable with rate of 0.7 downs/hour. What is the probability that the repair time will take at most 2 hours given that the repair man has been working on the machine for 30 mins? Response: 0.37 

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Question 2 Commonly, car cooling systems are controlled by electrically driven fans. Assuming that the lifetime T in hours of a particular make of fan can be modeled by an exponential distribution with λ = 0.0003. Find the proportion of fans which will give at most 1000 hours service. Response: 0.950 

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Question 3 Break downs occur on an old car with rate λ= 5 break -downs/month.

The owner of the car is  planning to have a trip on his car for 4 days.What is the probability that he will return home safely on his car. (Use the conversion of 30 days in a month.) Response: 0.5314 

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Question 4 Suppose you usually get 3 phone calls per hour. Compute the probability that a phone call will arrive within the next hour. Response: 0.283 

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Question 5 In a certain company, the secretary receives c alls at an average rate of 10 per hour. Find the  probability that a call will occur in the next 5 minutes given that you have already waited 10 minutes for a call. Response: 0.2835 

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Question 1 A sugar refinery has three processing plants, all receiving raw sugar in bulk. The amount of raw sugar (in tons) that one plant can process in one day can be modeled using an exponential distribution with mean of 4 tons for each of three plants. If each plants operates independently, find the probability that any given plant processes less than 5 tons of raw sugar on a given day. Response: 0.5507 

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Question 2 The time required to repair a machine is an exponential random variable with rate of 0.7 downs/hour. What is the probability that the repair time will take at least 2 hours given that the repair man has been working on the machine for 45 mins? Response: 0.5712

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Question 3 In a local bar and restaurant, students arrive according to an exponential distribution at a mean rate of 20 students per hour. What is the probability that the waiter has to wait not more than 4 minutes to serve the next student? Response: 73.6% 

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Question 4 Commonly, car cooling systems are controlled by electrically driven fans. Assuming that the lifetime T in hours of a particular make of fan can be modeled by an exponential distribution with λ = 0.0003. Find the proportion of fans which will give at most 1000 hours service. Response: 0.330 

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Question 5 Suppose that the amount of time one spends in a bank is exponentially distributed with mean 20 minutes. What is the probability that a customer will spend more than 20 minutes in the bank given that he is still in the bank after 15 minutes? Response: 77.9%

Question 1 Suppose you usually get 3 phone calls per hour. Compute the probability that a phone call will arrive within the next hour. Response: 0.283 

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Question 2 Commonly, car cooling systems are controlled by electrically driven fans. Assuming that the lifetime T in hours of a particular make of fan can be modeled by an exponential distribution with λ = 0.0003. Find the proportion of fans which will give at most 1000 hours service. Response: 0.741

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Question 3 Suppose that the amount of time one spends in a bank is exponentially distributed with mean 20 minutes. What is the probability that a customer will spend more than 20 minutes in the bank given that he is still in the bank after 15 minutes? Response: 77.9% 

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Question 4 Break downs occur on an old car with rate λ= 5 break -downs/month. The owner of the car is planning to have a trip on his car for 4 days.What is the probability that he will return home safely on his car. (Use the conversion of 30 days in a month.)

Response: 0.5134 

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Question 5 Suppose that the distance that can covered by a particular car before its battery wears out is exponentially distributed with an average of 10,000 kilometers. The owner of the car needs to take a 5000-km trip. What is the probability that he will be able to complete the trip without having to replace the car battery? Response: 61%